Critical exponents of planar gradient percolation
نویسندگان
چکیده
منابع مشابه
CRITICAL EXPONENTS OF PLANAR GRADIENT PERCOLATION By Pierre Nolin École
We study gradient percolation for site percolation on the triangular lattice. This is a percolation model where the percolation probability depends linearly on the location of the site. We prove the results predicted by physicists for this model. More precisely, we describe the fluctuations of the interfaces around their (straight) scaling limits, and the expected and typical lengths of these i...
متن کاملCritical exponents for two-dimensional percolation
We show how to combine Kesten’s scaling relations, the determination of critical exponents associated to the stochastic Loewner evolution process by Lawler, Schramm, and Werner, and Smirnov’s proof of Cardy’s formula, in order to determine the existence and value of critical exponents associated to percolation on the triangular lattice.
متن کاملCritical exponents in percolation via lattice animals
We examine the percolation model by an approach involving lattice animals, divided according to their surface-area-to-volume ratio. Throughout, we work with the bond percolation model in Z. However, the results apply to the site or bond model on any infinite transitive amenable graph with inessential changes. For any given p ∈ (0, 1), two lattice animals with given size are equally likely to ar...
متن کاملPercolation critical exponents in scale-free networks.
We study the behavior of scale-free networks, having connectivity distribution P(k) approximately k(-lambda), close to the percolation threshold. We show that for networks with 3<lambda<4, known to undergo a transition at a finite threshold of dilution, the critical exponents are different than the expected mean-field values of regular percolation in infinite dimensions. Networks with 2<lambda<...
متن کاملPercolation thresholds, critical exponents, and scaling functions on planar random lattices and their duals.
The bond-percolation process is studied on periodic planar random lattices and their duals. The thresholds and critical exponents of the percolation transition are determined. The scaling functions of the percolating probability, the existence probability of the appearance of percolating clusters, and the mean cluster size are also calculated. The simulation result of the percolation threshold ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2008
ISSN: 0091-1798
DOI: 10.1214/07-aop375